1. Field of the Invention
The present invention relates to communications systems and, more particularly, to phase angle demodulators.
2. Description of the Related Technology
Most electronic communication systems in use today include a transmitter to transmit an electromagnetic signal and a receiver to receive the transmitted signal. The transmitted signal is typically corrupted by noise and, therefore, the receiver must operate with received data that reflects the combination of the transmitted signal and noise. Thus, the receiver receives data y(t) at a time t, where y(t)=s(t)+n(t), the sum of the transmitted signal and additive noise. The received data equation can be expanded as follows: ##EQU1## where A is the signal amplitude, .omega..sub.o is the carrier or reference frequency, .theta.(t) is the time-varying phase function and n(t) is noise.
Many of these communication systems require that the receiver demodulate information in the received signal which depends on proper demodulation of the signal phase angle at all times during transmission. The demodulation of the signal phase angle is problematic in view of the pervasiveness of noise. Therefore, for this class of receivers it is desirable to optimize phase demodulation, which is equivalent to optimizing an estimation of the phase function .theta.(t).
Analog communication involves modulation that varies monotonically with an applied signal, e.g., a change in frequency that is proportional to the voltage at the output of a microphone as is the case in frequency modulation (FM) radio. An analog FM signal can be analyzed by measuring the phase of the signal at a sequence of sampling times via in-phase and quadrature components, as described in the parent patent application, now having U.S. Pat. No. 5,303,269, which is hereby incorporated by reference. These components can be used to obtain a block of preliminary phase samples .alpha.(k.DELTA.), k=1,2, . . . ,N. A corresponding block of expected or prior mean phase samples .theta..sub.m (k.DELTA.), k=1,2, . . . ,N is also presumably available. The prior mean samples are predictions of phase angle based on past data.
The parent application shows how a Hopfield neural network can be used to solve for the maximum a posteriori (MAP) phase estimates {.theta.(k.DELTA.); k=1,2, . . . ,N} based on the preliminary phase samples {.alpha.(k.DELTA.); k=1,2, . . . ,N}, the corresponding prior mean or predicated phase samples {.theta..sub.m (k.DELTA.); k=1,2, . . . ,N}, and the expected autocovariance function of the estimated phase shifts, R.sub..theta. [(k-j).DELTA.], in a MAP demodulator. Ideally, the sample block is at least as long as the nonzero support of the autocovariance function. The most accurate phase estimate is obtained for the sample at the middle of the block. If the autocovariance function is nonzero over a set of 31 samples between (k-15).DELTA. and (k+15).DELTA., for example, then a block composed of 31 phase shift samples between (k-15).DELTA. and (k+15).DELTA. would be used to estimate .theta.(k.DELTA.). The output of the Hopfield network also contains phase samples between (k-15).DELTA. and (k+15).DELTA., but samples near the block edges are not as accurate as those near the center of the block. Thus, in a MAP demodulator, it is desired to increase the accuracy of phase estimates which are generated based upon blocks of phase samples using a MAP estimator and a mean phase estimator.